adjust rigid body objects' position without affecting the whole shape
I know my proposals are &quot;another&quot; alternative solution, but maybe it is enough for you.
Instead of moving around them manually you could e.g.
Proposal 1:

give them another mass and check whether you are satisfied with the new result. To do so: select all cubes, and choose another mass -&gt; and you got new positions


Proposal 2:

you manually put other weights to your cubes

Proposal 3:

this is what you want to do, but it is a LOT OF work.

you can bake your simulation to keyframes. Then you have control over each keyframe of your animation.
you can do it like this:

But the disadvantage is, that you have to change nearly every position of each keyframe for each cube so that it looks realistic.